June 1, 1917] 



SCIENCE 



553 



ieal reasoning is not now more commonly 

 used in scientific research. This may serve 

 to explain the following assertion recently 

 made by Professor H. S. White : 



Most scientists can and will become mathema- 

 ticians when their special problems reach the 

 stage where measurements are possible.* 



It may be desirable to direct attention to 

 the fact that the mathematician might al- 

 most be said to cease to be a mathematician 

 when he becomes an investigator. It is 

 true that he needs a large and growing 

 amount of mathematical knowledge in order 

 to investigate successfully. The flood of 

 valueless literatux'e contributed in recent 

 years by non-mathematicians who endeav- 

 ored to solve the great prize problem, known 

 as the Greater Fermat Problem, has empha- 

 sized the fact that, in mathematics, as well 

 as in other sciences, 



important advances in knowledge are far more 

 likely to issue from the expert than from -the in- 

 expert. Indeed, the probability of extending 

 knowledge by organizations conducted by disci- 

 plined investigators ia so much greater than the 

 probability of extending knowledge by the drag- 

 net method that we not only may but should ig- 

 nore the latter in comparison with the former.s 



The mathematical investigator can clearly 

 not afford to forget his knowledge of mathe- 

 matics, but it is questionable whether he can 

 afford to confine himself to mathematical 

 reasoning while he is aiming to advance his 

 subject. He needs imagination and ability 

 to foresee results long before his mathe- 

 matical machinery has enabled him to es- 

 tablish them. Unless we become like chil- 

 dren in faith and fancy, we should not ex- 

 pect to add much that is fundamentally 

 new to the kingdom of mathematics. As in- 

 vestigators we all have much more in com- 

 mon than as students of what has been done 

 by others, and this common ground natu- 



4H. S. White, Science, N. S., Vol. 43 (1916), 

 p. 587. 



5E. S. Woodward, Science, N. S., Vol. 40 

 (1914), p. 221. 



rally increases with the originality of our 

 investigations. 



This common ground of investigators 

 may serve to explain the fact that many of 

 the most influential research organizations, 

 like the National Academy of Sciences in 

 our own country, embrace all the sciences. 

 In recent decades there has been a tendency 

 to organize research separately in the vari- 

 ous subjects in the form of national societies 

 named after these subjects. In fact, there 

 are those who think that the latter have as- 

 sumed such a preponderant sphere of in- 

 fluence as to threaten the vei-y life of the 

 former as serious factors in research. On 

 the other hand, the maintenance of a com- 

 mon scientific life seems to be of the high- 

 est importance in view of desirable interac- 

 tions and special emphasis on what is most 

 fundamental. 



The history of mathematics has taught 

 us that some subjects which were appar- 

 ently far apart and which were long de- 

 veloped separately were later seen to have 

 most important common elements. The 

 discovery of these common elements and 

 their development has led to marked ad- 

 vances in the separate fields themselves. 

 By way of illustration I need only refer to 

 the fields of algebra and geometry so hap- 

 pily welded through the work of Descartes, 

 Fermat and many others. In modern times 

 the theory of groups and invariants has ex- 

 hibited many important connections be- 

 tween subjects which had been supposed to 

 be widely separated. The same tendency 

 has, of course, manifested itself in other 

 sciences and may be assumed to become 

 more dominant as knowledge advances. 



A pertinent difference between the mathe- 

 matical investigatoi-s and investigators in 

 other sciences is that the former are com- 

 pelled to stay with their problems imtil a 

 solution is reached which can be proved to 

 be in accord with deductions from certain 

 definite assumptions, while the latter enjoy 



